
import pandas as pd
import numpy as np
import statsmodels.api as sm
import datetime
import matplotlib.pyplot as plt
from sklearn.covariance import LedoitWolf
from IPython.display import display, HTML
import warnings
warnings.filterwarnings('ignore')


# Pull the list of utility stock tickers from wikepedia
# store them in utlilities tickers
import requests
url = "https://en.wikipedia.org/wiki/List_of_S%26P_500_companies"
response = requests.get(url)
text = response.text
from bs4 import BeautifulSoup
soup = BeautifulSoup(text)
tag_list = soup.find_all("tr")
utilities_tickers = list()
for tag in tag_list:
    try:
        if tag.find_all('td')[2].get_text() == 'Utilities':
            utilities_tickers.append(tag.find_all('td')[0].get_text().replace("\n", ""))        
    except IndexError:
        pass


import datetime as dt
from pandas_datareader import data as pdr
import yfinance as yfin

yfin.pdr_override()

start_date = dt.datetime(1960, 1, 1)
end_date = dt.datetime(2023, 1, 1)

utilities_stock_data = dict()

for ticker in utilities_tickers:
    df = pdr.get_data_yahoo(ticker, start=start_date, end=end_date)
    df = df.reset_index()
    df['Date'] =  pd.to_datetime(df['Date'])
    utilities_stock_data[ticker] = df

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monthly_spy_data = pd.read_csv('./SPY.csv', index_col='Date', parse_dates=True)
monthly_spy_data['Monthly_Return'] = monthly_spy_data['Adj Close'].pct_change(periods=1)
monthly_spy_data.index = monthly_spy_data.index - pd.DateOffset(days=1)
monthly_spy_data = monthly_spy_data.drop(monthly_spy_data.tail(5).index)
monthly_spy_data


# utilities data
for ticker in utilities_stock_data:
    utilities_stock_data[ticker]= utilities_stock_data[ticker].set_index('Date')
    utilities_stock_data[ticker] = utilities_stock_data[ticker].resample('M').last()
    utilities_stock_data[ticker]['pct change'] = utilities_stock_data[ticker]['Adj Close'].pct_change()


pop = ['AES', 'AEE', 'CEG', 'AWK', 'CMS', 'FE', 'NRG', 'SRE'] # cutoff around ~400 months of data
for p in pop: 
    utilities_stock_data.pop(p)


# store data in dataframe
data = {}
for ticker in utilities_stock_data:
    data[ticker] = utilities_stock_data[ticker]['pct change']
utilities_returns = pd.DataFrame(data)
utilities_returns = utilities_returns.set_index(utilities_stock_data['AEP'].index)
utilities_returns = utilities_returns.iloc[1: , :]
utilities_returns = utilities_returns.dropna()
utilities_returns


factor_df = pd.read_csv('./factor_FF_devil.csv', index_col=0)
factor_df.index = pd.to_datetime(factor_df.index, format='%Y%m') + datetime.timedelta(days=-1)
factor_df['HML devil'] = factor_df['HML devil']*100
factor_df = factor_df/100
factor_df


def sampleMeanVariant(sigmahat, muhat, rf, kappa):
    e = np.ones((sigmahat.shape[0], 1))
    H = (muhat - rf*e).T @ np.linalg.inv(sigmahat) @ (muhat - rf*e)
    aStar = (kappa-rf)/H * np.linalg.inv(sigmahat) @ (muhat - rf*e)
    return aStar


sampleMeanVariant(np.cov(utilities_returns, rowvar=False), np.array([np.mean(utilities_returns, axis=0)]).T, factor_df['RF'][-1], 0.012)

array([[ 0.01174723],
       [-0.16453512],
       [ 0.24406775],
       [-0.02551994],
       [-0.13859163],
       [ 0.08812135],
       [ 0.19309851],
       [-0.01928269],
       [ 0.04250492],
       [-0.12286952],
       [-0.22672308],
       [-0.01627721],
       [ 0.00435655],
       [ 0.44437863],
       [-0.0012304 ],
       [-0.00887804],
       [-0.05948933],
       [-0.04751013],
       [ 0.01659133],
       [ 0.43326368],
       [ 0.21510329],
       [ 0.00996532]])


def factorModel(returns, factorDF, rf, kappa, numFactors):
    """ 
    returns - monthly returns dataframe of each equity (m,d)
    factorDF - df of excess market returns, SMB, HML
    rf - series of rf rate
    kappa - targeted expected return for portfolio
    numFactors - the number of factors in the model
    """

    d = returns.shape[1]
    # Compute the excess returns of each asset
    excess_returns = returns.sub(rf,axis=0).values

    # Define arrays to store the beta coefficients and residual variances
    betas = np.zeros((d, numFactors))
    residual_variances = np.zeros((d))

    # Perform the OLS regression for each asset
    for i in range(d):
        # Extract the excess returns of the i-th asset
        excess_asset_returns = excess_returns[:,i]

        # Define the OLS model with the R-rf ~ MF-rf + SMB + HML
        model = sm.OLS(excess_asset_returns,
                       sm.add_constant(factorDF))

        # Fit the model and extract the regression coefficients and residuals
        results = model.fit()
        beta = results.params[1:]
        residuals = results.resid

        # Store the beta coefficients and residual variance for the i-th asset
        betas[i] = beta
        residual_variances[i] = np.var(residuals, ddof=numFactors + 1)
        
    sigmaFactor = np.cov(factorDF.T)
    Dhat = np.diag(residual_variances)
    sigmahat = betas@sigmaFactor@betas.T + Dhat
    muhat = returns.mean().values.reshape((-1, 1))
    
    # pass most recent rf 
    return sampleMeanVariant(sigmahat, muhat, rf[-1], kappa)


AF_factorDF = factor_df[['MKT', 'SMB', 'HML devil']].loc['1/31/1984':'12/31/2022']
rf_DF = factor_df['RF'].loc['1/31/1984':'12/31/2022']
AF_a = factorModel(utilities_returns, AF_factorDF, rf_DF, kappa=.012,numFactors=3)
AF_a

array([[0.05654647],
       [0.05334952],
       [0.06741343],
       [0.0371012 ],
       [0.07089734],
       [0.06932758],
       [0.08302917],
       [0.05912089],
       [0.03889345],
       [0.04043529],
       [0.03750989],
       [0.05049437],
       [0.04955986],
       [0.08639314],
       [0.0401979 ],
       [0.01763947],
       [0.01730354],
       [0.04307185],
       [0.0556642 ],
       [0.08926318],
       [0.09038271],
       [0.04852111]])


FF_factorDF = factor_df[['MKT', 'SMB', 'HML FF']].loc['1/31/1984':'12/31/2022']
FF_a = factorModel(utilities_returns, FF_factorDF, rf_DF, kappa=.012, numFactors=3)
FF_a

array([[0.05600936],
       [0.05145666],
       [0.06533542],
       [0.03636784],
       [0.07341181],
       [0.06781274],
       [0.08185201],
       [0.05743151],
       [0.03332141],
       [0.03908481],
       [0.04074068],
       [0.04976133],
       [0.04944596],
       [0.08998026],
       [0.04390553],
       [0.01530909],
       [0.01856316],
       [0.04291205],
       [0.05801989],
       [0.0884523 ],
       [0.0907776 ],
       [0.05109328]])


def stein_wolf(returns, rf, params):
    kappa = params[0]
    mu_hat = np.mean(returns, axis=0)
    sigma_hat = np.cov(returns, rowvar=False)
    e = np.ones(len(mu_hat))
    d = len(returns.columns)
    N = len(returns)
    
    mu_0 = ((mu_hat.T @ np.linalg.inv(sigma_hat) @ e)/(e.T @ np.linalg.inv(sigma_hat) @ e)) * e
    alpha = (d + 2) / (d + 2 + (N - d - 2) * ((mu_hat - mu_0).T @ np.linalg.inv(sigma_hat) @ (mu_hat - mu_0)))
    shrunk_mean = (alpha * mu_0) + ((1 - alpha) * mu_hat)
    
    cov = LedoitWolf().fit(returns)
    shrunk_var = cov.covariance_
    
    return sampleMeanVariant(shrunk_var, np.array([shrunk_mean]).T, rf[-1], kappa)


stein_wolf(utilities_returns, rf_DF, [0.012])

array([[ 0.10207668],
       [-0.14515308],
       [ 0.24536392],
       [-0.07190104],
       [ 0.0497614 ],
       [ 0.1951668 ],
       [ 0.14421587],
       [ 0.00491196],
       [ 0.04215468],
       [-0.11209936],
       [-0.02282054],
       [ 0.07205937],
       [ 0.01451278],
       [ 0.19992312],
       [ 0.03772774],
       [ 0.03048986],
       [-0.04449797],
       [ 0.04216621],
       [-0.04717335],
       [ 0.23621698],
       [ 0.18165808],
       [ 0.00605032]])


def equal_weights(returns, rf, params):
    a = np.repeat(1/len(returns.columns), len(returns.columns))
    return a


equal_weights(utilities_returns, factor_df['RF'], [])

array([0.04545455, 0.04545455, 0.04545455, 0.04545455, 0.04545455,
       0.04545455, 0.04545455, 0.04545455, 0.04545455, 0.04545455,
       0.04545455, 0.04545455, 0.04545455, 0.04545455, 0.04545455,
       0.04545455, 0.04545455, 0.04545455, 0.04545455, 0.04545455,
       0.04545455, 0.04545455])


def roll(d, M, T, returns, method, params):
    '''
    d: number of assets
    M: size of window in terms of months
    T: total number of periods
    returns: T x d dataframe of returns for d assets for T total periods
    method: function that computes allocation weights
    params: parameters needed for allocation method
    '''

    X = np.zeros(T-M)
    dates = pd.to_datetime(returns.index)
    Rf = np.zeros(T-M)
    
    for t in range(M,T):
        # get training and testing set
        start = dates[t-M]
        end = dates[t]
        R_train = returns.loc[start:end]
        R_test = returns.loc[end]
        rf = factor_df['RF'].loc[start:end]
        
        # get allocation weights
        a = method(R_train, rf, params)
    
        # get return of next period
        X[t-M], Rf[t-M] = a.T @ R_test + (1 - np.sum(a)) * rf[-1], rf[-1]
    
    return X, Rf


def roll_factor(d, M, T, returns, factors, k=0.012):
    '''
    d: number of assets
    M: size of window in terms of months
    T: total number of periods
    returns: T x d dataframe of returns for d assets for T total periods
    factors: factors to be used in factor model
    '''
       
    X = np.zeros(T-M)
    dates = pd.to_datetime(returns.index)
    Rf = np.zeros(T-M)

    for t in range(M,T):
        # get training and testing set
        start = dates[t-M]
        end = dates[t]
        R_train = returns.loc[start:end]
        R_test = returns.loc[end]
        rf = factor_df['RF'].loc[start:end]
        
        # get allocation weights
        a = factorModel(R_train, factor_df[factors].loc[start:end], rf, kappa=k, numFactors=len(factors))
    
        # get return of next period
        X[t-M], Rf[t-M] = a.T @ R_test + (1 - np.sum(a)) * rf[-1], rf[-1]

    return X, Rf


d = len(utilities_returns.columns)
M_range = [6, 1*12, 2*12, 5*12] # 1, 2, 5, 8, 10, year windows
T = len(utilities_returns)
k = 0.012


def get_performance_metrics(X, Rf):
    risk_premium = X - Rf
    ORTN = np.mean(risk_premium)
    OSR = np.mean(risk_premium)/np.std(risk_premium)
    return [ORTN, OSR] # return, sharpe ratio


def compare_FF_devil(factors, horizon, plot_equal, plot_market, k=0.012):
    '''
    factors: a list of factors without HML
    horizon: investment horizon in terms of years
    '''
    
    FF_factors = factors.copy()
    FF_factors.append('HML FF')
    AF_factors = factors.copy()
    AF_factors.append('HML devil')
    rf = factor_df['RF'][-1]
    
    for m in M_range:
        # factor model
        FF, Rf_FF = roll_factor(d, m, T, utilities_returns, FF_factors, k)
        
        AF, Rf_AF = roll_factor(d, m, T, utilities_returns, AF_factors, k)

        # stein wolf
        SW, Rf_SW = roll(d, m, T, utilities_returns, stein_wolf, [k])
        
        # benchmark 1
        equal, Rf_EW = roll(d, m, T, utilities_returns, equal_weights, [])
        
        # benchmark 2
        market = np.concatenate((np.repeat(monthly_spy_data['Monthly_Return'].iloc[1],len(FF)-len(monthly_spy_data)+2), monthly_spy_data['Monthly_Return'].iloc[1:-1]))
        
        # rolling of rolling
        df = pd.DataFrame({'FF':FF, 
                           'AF':AF, 
                           'SW': SW,
                           'EW': equal,
                           'SP':market})
        df = df.rolling(horizon * 12).mean()

        # performance metrics
        PM_FF = get_performance_metrics(FF, Rf_FF)
        PM_FF.append(df.mean(axis=0)['FF'])
        PM_AF = get_performance_metrics(AF, Rf_AF)
        PM_AF.append(df.mean(axis=0)['AF'])
        PM_SW = get_performance_metrics(SW, Rf_SW)
        PM_SW.append(df.mean(axis=0)['SW'])
        PM_EW = get_performance_metrics(equal, Rf_EW)
        PM_EW.append(df.mean(axis=0)['EW'])
        PM_SP = get_performance_metrics(market, Rf_FF)
        PM_SP.append(df.mean(axis=0)['SP'])

        df_metrics = pd.DataFrame({'FF': PM_FF, 
                                  'AF': PM_AF,
                                  'Stein-Wolf': PM_SW,
                                  'Equal Weights': PM_EW, 
                                  'S&P 500': PM_SP},
                                  ['ORTN', 'OSR', 'MMAR'])
        df_metrics = df_metrics.style.set_caption('Performance Metrics')
        display(df_metrics)
        
        # plotting
        plt.plot(utilities_returns.index[m:], df['FF'], label='FF ' + str(len(factors)+1) + '-Factor')
        plt.plot(utilities_returns.index[m:], df['AF'], label='AF ' + str(len(factors)+1) + '-Factor')
        plt.plot(utilities_returns.index[m:], df['SW'], label='Stein-Wolf')
       
        # plt.axhline(y = df.mean(axis=0)['FF'], color = 'blue', alpha=0.66, linestyle = 'dashed')
        # plt.axhline(y = df.mean(axis=0)['AF'], color = 'orange', alpha=0.66, linestyle = 'dashed')
        # plt.axhline(y = df.mean(axis=0)['SW'], color = 'green', alpha=0.66, linestyle = 'dashed')
        
        if plot_equal:
            plt.plot(utilities_returns.index[m:], df['EW'], label='BM: Equal Weights')
            #plt.axhline(y = df.mean(axis=0)['Equal Weights'], color = 'purple', alpha=0.66, linestyle = 'dashed')
        if plot_market:
            plt.plot(utilities_returns.index[m:], df['SP'], label='BM: S&P 500')
            #plt.axhline(y = df.mean(axis=0)['S&P 500'], color = 'red', alpha=0.66, linestyle = 'dashed')

        plt.suptitle('Avg. Monthly Return Over ' + str(horizon) + '-Year Investment from Utilities Stocks in the S&P 500')
        plt.title('Rolling Window of Size ' + str(m) + ' Months')
        plt.legend()
        plt.ylabel('Return')
        plt.xlabel('End of ' + str(horizon) + '-year Investment')
        plt.show()


# 3 factor with BM
compare_FF_devil(['MKT','SMB'], 10, 1, 1, 0.0117)


# 3 factor w/o BM
compare_FF_devil(['MKT','SMB'], 10, 0, 0, 0.0117)


# ff 5-factor with BM
compare_FF_devil(['MKT','SMB','RMW','CMA'], 10, 1, 1, 0.0117)


# ff 5-factor w/o BM
compare_FF_devil(['MKT','SMB','RMW','CMA'], 10, 0, 0, 0.0117)


# aqr 5-factor with BM
compare_FF_devil(['MKT','SMB','MOM','STR'], 10, 1, 1, 0.0117)


# aqr 5-factor w/o BM
compare_FF_devil(['MKT','SMB','MOM','STR'], 10, 0, 0, 0.0117)


# 6-factor with BM
compare_FF_devil(['MKT','SMB','RMW','CMA','MOM'], 10, 1, 1, 0.0117)


# 6-factor w/o BM
compare_FF_devil(['MKT','SMB','RMW','CMA','MOM'], 10, 0, 0, 0.0117)

	Open	High	Low	Close	Adj Close	Volume	Monthly_Return
Date
1993-01-31	43.968750	45.125000	42.812500	44.406250	25.390364	5417600	NaN
1993-02-28	44.562500	45.843750	44.218750	45.187500	25.837070	3019200	0.017594
1993-03-31	45.250000	45.250000	43.281250	44.031250	25.294857	2697200	-0.020986
1993-04-30	44.093750	45.656250	43.843750	45.218750	25.977036	1808000	0.026969
1993-05-31	45.375000	45.812500	44.218750	45.062500	25.887280	3438000	-0.003455
...	...	...	...	...	...	...	...
2022-08-31	392.890015	411.730011	357.040009	357.179993	352.746490	1998908600	-0.096159
2022-09-30	361.079987	389.519989	348.109985	386.209991	382.982941	2024732000	0.085717
2022-10-31	390.140015	407.679993	368.790009	407.679993	404.273560	1745985300	0.055592
2022-11-30	408.769989	410.489990	374.769989	382.429993	379.234528	1735973600	-0.061936
2022-12-31	384.369995	408.160004	377.829987	406.480011	404.934570	1575450100	0.067768

	LNT	AEP	ATO	CNP	ED	D	DTE	DUK	EIX	ETR	...	EXC	NEE	NI	PCG	PNW	PPL	PEG	SO	WEC	XEL
Date
1984-01-31	0.000000	0.072993	0.000000	0.032257	0.010101	0.067797	0.018182	-0.009950	-0.025157	0.009345	...	0.043477	-0.009317	-0.034188	0.008403	-0.006452	0.042425	0.027473	-0.003139	0.004546	-0.026315
1984-02-29	-0.035087	-0.052498	0.022555	-0.028244	-0.070189	-0.095238	0.000000	-0.068241	-0.054839	0.037037	...	-0.012877	-0.065570	-0.008850	-0.075000	-0.019480	0.005813	-0.083845	-0.055118	-0.072398	-0.027028
1984-03-31	-0.059091	-0.029630	0.029412	0.019867	0.054945	0.011696	-0.051107	0.060773	-0.004815	-0.032157	...	0.008771	0.020619	-0.017857	-0.043466	-0.046358	-0.057803	-0.012048	0.025000	0.014634	-0.031250
1984-04-30	0.019324	0.007633	-0.057142	0.025974	0.031250	0.080925	-0.058253	-0.015625	0.056338	-0.057143	...	-0.104348	0.026936	0.000000	0.029126	-0.104167	0.018405	0.085366	0.008129	0.028846	0.025090
1984-05-31	0.004739	-0.019454	0.000000	-0.026792	0.016500	-0.069519	0.041237	-0.002048	-0.033333	0.020203	...	-0.008135	-0.034739	-0.063636	0.018868	0.062016	0.054217	-0.028090	-0.036544	0.009345	0.024475
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2022-08-31	0.001805	0.024625	-0.060576	0.000436	-0.007595	-0.002196	0.000307	-0.018510	0.000000	0.009997	...	-0.048458	0.011629	-0.029276	0.135359	0.025589	0.000000	-0.019948	0.011168	0.000471	0.014621
2022-09-30	-0.131881	-0.137225	-0.101693	-0.106248	-0.122570	-0.148178	-0.111286	-0.129922	-0.155475	-0.127233	...	-0.146891	-0.078180	-0.146391	0.013788	-0.143862	-0.121587	-0.119246	-0.117685	-0.132926	-0.132408
2022-10-31	-0.007126	0.017004	0.046146	0.015259	0.025653	0.012444	-0.025554	0.001720	0.061152	0.064693	...	0.030166	-0.011606	0.029384	0.194400	0.055218	0.044970	-0.002845	-0.037059	0.021246	0.017344
2022-11-30	0.079164	0.111336	0.135193	0.094143	0.124543	-0.126626	0.034787	0.083559	0.110260	0.096165	...	0.081385	0.098454	0.087583	0.051574	0.165303	0.114383	0.079900	0.043922	0.094332	0.078482
2022-12-31	-0.019361	-0.019112	-0.067637	-0.036001	-0.027846	0.014526	0.021274	0.030621	-0.034648	-0.032425	...	0.044960	-0.012987	-0.018611	0.035669	-0.029111	-0.002417	0.021088	0.055736	-0.054267	0.005288

	MKT	SMB	HML FF	HML devil	RMW	CMA	RF	MOM	STR
Date
1963-06-30	-0.0039	-0.0041	-0.0097	-0.0059	0.0068	-0.0118	0.0027	0.0090	-0.0008
1963-07-31	0.0507	-0.0080	0.0180	0.0028	0.0036	-0.0035	0.0025	0.0101	0.0130
1963-08-31	-0.0157	-0.0052	0.0013	0.0027	-0.0071	0.0029	0.0027	0.0019	0.0119
1963-09-30	0.0253	-0.0139	-0.0010	-0.0211	0.0280	-0.0201	0.0029	0.0312	-0.0066
1963-10-31	-0.0085	-0.0088	0.0175	0.0091	-0.0051	0.0224	0.0027	-0.0074	0.0112
...	...	...	...	...	...	...	...	...	...
2022-08-31	-0.0935	-0.0097	0.0006	-0.0274	-0.0151	-0.0084	0.0019	0.0347	-0.0161
2022-09-30	0.0783	0.0186	0.0805	0.0502	0.0307	0.0652	0.0023	0.0387	0.0033
2022-10-31	0.0460	-0.0267	0.0138	0.0241	0.0601	0.0311	0.0029	-0.0201	0.0055
2022-11-30	-0.0641	-0.0016	0.0132	-0.0044	0.0009	0.0419	0.0033	0.0452	-0.0342
2022-12-31	0.0665	0.0443	-0.0405	0.0476	-0.0262	-0.0453	0.0035	-0.1598	0.0937

	FF	AF	Stein-Wolf	Equal Weights	S&P 500
ORTN	0.009030	0.009216	0.009181	0.007889	0.007991
OSR	1.264365	1.353326	2.267006	0.184906	0.206700
MMAR	0.011609	0.011809	0.011758	0.009764	0.009657

	FF	AF	Stein-Wolf	Equal Weights	S&P 500
ORTN	0.009438	0.009414	0.009680	0.007633	0.007968
OSR	0.757602	0.748519	1.499537	0.178207	0.204765
MMAR	0.011847	0.011842	0.012029	0.009719	0.009552

1 Get data¶

1.1 Get utilities in S&P data¶

1.2 Get factor data¶

2 Allocation Methods¶

2.1 Mean-Variance¶

2.2 Method 1: Factor Model¶

2.3 Method 2: James-Stein with Ledoit Wolf¶

2.3 Benchmark: 1/n¶

3 Rolling Window¶

4 Simulation¶

Things to Look into:¶

Needed from code perspective:¶

	FF	AF	Stein-Wolf	Equal Weights	S&P 500
ORTN	0.008275	0.008158	0.018793	0.007429	0.007874
OSR	0.395090	0.397392	0.456066	0.173243	0.199688
MMAR	0.010323	0.010270	0.022434	0.009647	0.009326

	FF	AF	Stein-Wolf	Equal Weights	S&P 500
ORTN	0.009186	0.009351	0.019122	0.007597	0.007446
OSR	0.257708	0.262761	0.517912	0.178725	0.181125
MMAR	0.011867	0.011954	0.021978	0.009532	0.008438

	FF	AF	Stein-Wolf	Equal Weights	S&P 500
ORTN	0.009127	0.009171	0.009181	0.007889	0.007991
OSR	1.712918	1.829175	2.267005	0.184906	0.206700
MMAR	0.011620	0.011723	0.011758	0.009764	0.009657

	FF	AF	Stein-Wolf	Equal Weights	S&P 500
ORTN	0.009390	0.009420	0.009680	0.007633	0.007968
OSR	0.887208	0.880773	1.499537	0.178207	0.204765
MMAR	0.011677	0.011659	0.012029	0.009719	0.009552

	FF	AF	Stein-Wolf	Equal Weights	S&P 500
ORTN	0.008368	0.008345	0.018793	0.007429	0.007874
OSR	0.450301	0.450284	0.456096	0.173243	0.199688
MMAR	0.010377	0.010388	0.022434	0.009647	0.009326

	FF	AF	Stein-Wolf	Equal Weights	S&P 500
ORTN	0.009437	0.009499	0.019122	0.007597	0.007446
OSR	0.275000	0.278442	0.517912	0.178725	0.181125
MMAR	0.012036	0.012014	0.021978	0.009532	0.008438

	FF	AF	Stein-Wolf	Equal Weights	S&P 500
ORTN	0.009258	0.009124	0.009181	0.007889	0.007991
OSR	1.976301	1.987609	2.267005	0.184906	0.206700
MMAR	0.011977	0.011790	0.011758	0.009764	0.009657

	FF	AF	Stein-Wolf	Equal Weights	S&P 500
ORTN	0.009616	0.009684	0.009680	0.007633	0.007968
OSR	0.910463	0.906989	1.499537	0.178207	0.204765
MMAR	0.012024	0.012043	0.012029	0.009719	0.009552

	FF	AF	Stein-Wolf	Equal Weights	S&P 500
ORTN	0.008645	0.008522	0.018793	0.007429	0.007874
OSR	0.461676	0.455831	0.456096	0.173243	0.199688
MMAR	0.010604	0.010541	0.022434	0.009647	0.009326

	FF	AF	Stein-Wolf	Equal Weights	S&P 500
ORTN	0.009690	0.009711	0.019122	0.007597	0.007446
OSR	0.288782	0.288543	0.517912	0.178725	0.181125
MMAR	0.012213	0.012223	0.021978	0.009532	0.008438

	FF	AF	Stein-Wolf	Equal Weights	S&P 500
ORTN	0.009431	0.009418	0.009680	0.007633	0.007968
OSR	0.928292	0.929859	1.499537	0.178207	0.204765
MMAR	0.011719	0.011681	0.012029	0.009719	0.009552

	FF	AF	Stein-Wolf	Equal Weights	S&P 500
ORTN	0.008754	0.008618	0.018793	0.007429	0.007874
OSR	0.496899	0.486006	0.456096	0.173243	0.199688
MMAR	0.010715	0.010679	0.022434	0.009647	0.009326

	FF	AF	Stein-Wolf	Equal Weights	S&P 500
ORTN	0.009793	0.009791	0.019122	0.007597	0.007446
OSR	0.294743	0.296314	0.517912	0.178725	0.181125
MMAR	0.012271	0.012263	0.021978	0.009532	0.008438